Oscillatory integrals and multiplier problem for the disc

Lennart Carleson; Per Sjölin

Displaying similar documents to “Oscillatory integrals and multiplier problem for the disc”

On oscillatory integral operators with folding canonical relations

Allan Greenleaf, Andreas Seeger (1999)

Studia Mathematica

Similarity:

Sharp $L^{p}$ estimates are proven for oscillatory integrals with phase functions Φ(x,y), (x,y) ∈ X × Y, under the assumption that the canonical relation $C_{Φ}$ projects to T*X and T*Y with fold singularities.

$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains

Yibiao Pan, Gary Sampson, Paweł Szeptycki (1997)

Studia Mathematica

Similarity:

We prove the $L^{p}$ boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function ${| x |}^{α} {| y |}^{β}$ . Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.

Singular integrals on product H spaces.

Robert Fefferman (1985)

Revista Matemática Iberoamericana

Similarity:

$L^{2}$ Estimates for Oscillatory Integrals

G. Sampson (1998)

Colloquium Mathematicae

Similarity:

On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

Similarity:

A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators....

Fourier analysis in several parameters.

Robert Fefferman (1986)

Revista Matemática Iberoamericana

Similarity:

Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on R [1].

Variants of the Calderón-Zygmund theory for L-spaces.

Anthony Carbery (1986)

Revista Matemática Iberoamericana

Similarity:

The purposes of this paper may be described as follows: (i) to provide a useful substitute for the Cotlar-Stein lemma for L^p-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions); (ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed? (iii) to simplify and extend the work of Duoandikoetxea...

Hardy spaces and oscillatory singular integrals.

Yibiao Pan (1991)

Revista Matemática Iberoamericana

Similarity:

Calderón-Zygmund operators on product spaces.

Jean-Lin Journé (1985)

Revista Matemática Iberoamericana

Similarity:

An oscillatory singular integral operator with polynomial phase

Josfina Alvarez, Jorge Hounie (1999)

Studia Mathematica

Similarity:

We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space $H_{P}^{1}$ related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.